SpaceBanter.com - View Single Post - formula for astronomical midnight at Greenwich, in UT?

**Greg Neill[_6_]** · September 21st 10, 06:00 PM posted to sci.astro.amateur,uk.sci.astronomy

wrote:
Hi, I mentioned this in another thread but thought I'd give it a
thread of its own.

Can someone help with a formula for astronomical midnight at
Greenwich, in UT, given the Julian Day Number? I.e. the UT of the
first astronomical midnight (lower culmination of the apparent Sun)
following JDN = x.

Ideally I need an accuracy of a few seconds.

Many thanks in advance.

Michael

For that kind of accuracy, perhaps you could approach
it via the equation of time. Meeus (Astronomical
Algorithms) gives a method for determining the E of T
for a given date (Julian day).

Roughly, the procedure would be:

1. Determine the JD corresponding to Julian midnight for
the day in question.
2. Determine the E of T for that date from the JD and
Meeus' method(s).
3. Adjust the JD by the amount of the E of T.
4. Convert the JD into a UT.

The determination of the E of T involves determining the
Sun's mean anomaly, its apparent right ascention,
nutation, and the obliquity of the ecliptic. It's best
that you refer to the book for the mehtods involved,
since it would be tedious to reproduce the formulae
here in ascii.